Reduced models for rarefied gases and geophysical flows using moment hierarchies

Abstract

The high dimension of many mathematical models in science and engineering leads to prohibitively large computational cost for even an approximate numerical solution. However, an accurate solution of the full model is often not even necessary, as only a small set of variables suffices to characterise the main behaviour of the solution. This poses the question of model reduction: How can we efficiently reduce the complexity of the model and arrive at a reduced model, that is both sufficiently accurate and computationally feasible?

In this talk, we fist briefly discuss different model reduction techniques for kinetic equations. We then focus on moment models as one way to reduce the full model to a set of analytical, lower-dimensional equations. The benefits of moment models are the mathematically sound derivation, their hierarchical structure, and the possibility to assess analytical properties of the model from the resulting equations.

We consider, among other, examples from rarefied gases and free-surface flows and illustrate those by numerical simulations.

About the Speaker

Julian Koellermeier

University of Groningen

I am an assistant professor for model reduction and numerical simulation in applications like rarefied gases and free-surface flows. I started at the Bernoulli Institute of the University of Groningen in 2022 after postdoctoral positions at KU Leuven, Peking University and Free University Berlin and his PhD at RWTH Aachen University.